3/x-1-4 eching

$$\frac { 3 } { x - 1 } - 4$$

Baholash

$$\frac{7-4x}{x-1}$$

Qisqa yechim qadamlari

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 4 ni \frac{x-1}{x-1} marotabaga ko'paytirish.

$$\frac{3}{x-1}-\frac{4\left(x-1\right)}{x-1}$$

\frac{3}{x-1} va \frac{4\left(x-1\right)}{x-1} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{3-4\left(x-1\right)}{x-1}$$

3-4\left(x-1\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{3-4x+4}{x-1}$$

3-4x+4 kabi iboralarga o‘xshab birlashtiring.

$$\frac{7-4x}{x-1}$$

x ga nisbatan hosilani topish

$$-\frac{3}{\left(x-1\right)^{2}}$$

Koeffitsient uchun derivativ qoidasidan foydalanish qadamlari

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 4 ni \frac{x-1}{x-1} marotabaga ko'paytirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3}{x-1}-\frac{4\left(x-1\right)}{x-1})$$

\frac{3}{x-1} va \frac{4\left(x-1\right)}{x-1} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3-4\left(x-1\right)}{x-1})$$

3-4\left(x-1\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3-4x+4}{x-1})$$

3-4x+4 kabi iboralarga o‘xshab birlashtiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{7-4x}{x-1})$$

Har qanday ikki differensial funksiya uchun ikki funksiyaning koeffitsient hosilasi raqamlagichning hosila marotabasi maxraj minusi va barchasi kvadrat maxrajiga bo'lingan.

$$\frac{\left(x^{1}-1\right)\frac{\mathrm{d}}{\mathrm{d}x}(-4x^{1}+7)-\left(-4x^{1}+7\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{1}-1)}{\left(x^{1}-1\right)^{2}}$$

Polinomialning hosilasi bu uning shartlari hosilasining yig‘indisiga teng. Konstant shartning hosilasi 0. ax^{n} ning hosilasi nax^{n-1}.

$$\frac{\left(x^{1}-1\right)\left(-4\right)x^{1-1}-\left(-4x^{1}+7\right)x^{1-1}}{\left(x^{1}-1\right)^{2}}$$

Arifmetik hisobni amalga oshirish.

$$\frac{\left(x^{1}-1\right)\left(-4\right)x^{0}-\left(-4x^{1}+7\right)x^{0}}{\left(x^{1}-1\right)^{2}}$$

Distributiv xususiyatdan foydalanib kengaytirish.

$$\frac{x^{1}\left(-4\right)x^{0}-\left(-4x^{0}\right)-\left(-4x^{1}x^{0}+7x^{0}\right)}{\left(x^{1}-1\right)^{2}}$$

Ayni daraja ko'rsatkichlarini ko'paytirish uchun ularning darajalarini qo'shing.

$$\frac{-4x^{1}-\left(-4x^{0}\right)-\left(-4x^{1}+7x^{0}\right)}{\left(x^{1}-1\right)^{2}}$$

Arifmetik hisobni amalga oshirish.

$$\frac{-4x^{1}+4x^{0}-\left(-4x^{1}+7x^{0}\right)}{\left(x^{1}-1\right)^{2}}$$

Keraksiz qavslarni olib tashlash.

$$\frac{-4x^{1}+4x^{0}-\left(-4x^{1}\right)-7x^{0}}{\left(x^{1}-1\right)^{2}}$$

O'xshash hadlarni birlashtirish.

$$\frac{\left(-4-\left(-4\right)\right)x^{1}+\left(4-7\right)x^{0}}{\left(x^{1}-1\right)^{2}}$$

-4 dan -4 ni va 4 dan 7 ni ayiring.

$$\frac{-3x^{0}}{\left(x^{1}-1\right)^{2}}$$

Har qanday t sharti uchun t^{1}=t.

$$\frac{-3x^{0}}{\left(x-1\right)^{2}}$$

Har qanday t sharti uchun (0 bundan mustasno) t^{0}=1.

$$\frac{-3}{\left(x-1\right)^{2}}$$